Answer the questions based on the table given below concerning the busiest 20 international airports in the world International Airports Table
List of International Airports
| No. | Name | International Airport Type | Code | Location |
|---|---|---|---|---|
| 1 | Hartsfield | A | ATL | Atlanta, Georgia, USA |
| 2 | Chicago–O’Hare | A | ORD | Chicago, Illinois, USA |
| 3 | Los Angeles | A | LAX | Los Angeles, California, USA |
| 4 | Heathrow Airport | E | LHR | London, United Kingdom |
| 5 | DFW | A | DFW | Dallas/Ft. Worth, Texas, USA |
| 6 | Haneda Airport | F | HND | Tokyo, Japan |
| 7 | Frankfurt Airport | E | FRA | Frankfurt, Germany |
| 8 | Roissy–Charles de Gaulle | E | CDG | Paris, France |
| 9 | San Francisco | A | SFO | San Francisco, California, USA |
| 10 | Denver | A | DIA | Denver, Colorado, USA |
| 11 | Amsterdam Schiphol | E | AMS | Amsterdam, Netherlands |
| 12 | Minneapolis–St. Paul | A | MSP | Minneapolis–St. Paul, USA |
| 13 | Detroit Metropolitan | A | DTW | Detroit, Michigan, USA |
| 14 | Miami | A | MIA | Miami, Florida, USA |
| 15 | Newark | A | EWR | Newark, New Jersey, USA |
| 16 | McCarran | A | LAS | Las Vegas, Nevada, USA |
| 17 | Phoenix Sky Harbor | A | PHX | Phoenix, Arizona, USA |
| 18 | Kimpo | FE | SEL | Seoul, Korea |
| 19 | George Bush | A | IAH | Houston, Texas, USA |
| 20 | John F. Kennedy | A | JFK | New York, New York, USA |




| A | B | C | D | Average |
|---|---|---|---|---|
| 3 | 4 | 4 | ? | 4 |
| 3 | ? | 5 | ? | 4 |
| ? | 3 | 3 | ? | 4 |
| ? | ? | ? | ? | 4.25 |
| 4 | 4 | 4 | 4.25 |
For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: